emin: international master in economics and management of ... · ii_aux(i,i) nodes connected by a...

ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA – ICAI

Master Universitario en Sector Eléctrico(Erasmus Mundus)

EMIN: International Master in Economics and Management of Network Industries

“Decision support models in the electric

Andrés [email protected]

Session MOD.10

“Decision support models in the electric power industry”

Bulk system reliability

Bibliography

• IEEE Tutorial Course on Reliability Assessment of Composite Generation and Transmission Systems. IEEE October 1989

• EPRI Composite-system reliability evaluation. EPRI EL-5290. December 1987

• Rivier, M. (1998) Modelo probabilista de explotación de un sistema eléctrico: contribución a la teoría

2Master Universitario en Sector Eléctrico

(Erasmus Mundus)

Escuela Técnica Superior de Ingeniería – ICAIUniversidad Pontificia Comillas

de un sistema eléctrico: contribución a la teoría marginalista. Tesis doctoral. Universidad Pontificia Comillas.

• Sánchez, P. (1998) Mejoras en la eficacia computacional de modelos probabilistas de explotación generación/red a medio plazo. Tesis doctoral. Universidad Pontificia Comillas. (http://www.iit.upcomillas.es/aramos/tesis/tesis_PedroSanchez.pdf)

Content

�Motivation and applications

• Probabilistic operation models• Uncertainty modeling• Some models


(Erasmus Mundus)


Motivation

• To give an indication about what it is possible to state with a decision tool– Capabilities and limitations

• To become familiar with network modeling techniques


(Erasmus Mundus)


techniques

• To give the mathematical foundation

Long term applications

• Network expansion planning• Selection and evaluation of network investments

• Impact on the generation equipment and consumption


(Erasmus Mundus)


consumption• Interconnections

Medium term applications

• Traditional environment– Studies about network performance– Generation localization– Adequacy assessment/reliability studies– Network maintenance– Operation planning


(Erasmus Mundus)


– Operation planning

• TPA or open access– Check transfer capabilities– Determine payment for the network use– Assign network costs– Network remuneration studies– Evaluate network contracts

Short term applications

• Check the viability of the generation and consumption dispatch

• Determine nodal marginal prices• Identify and determine losses


(Erasmus Mundus)


• Identify and determine zonal or local ancillary services

• Decisions about network operation

Very short term applications

• Static analysis of the network– Flows– Voltages

• Dynamic analysis of the network– Stability


(Erasmus Mundus)


– Stability– Voltage collapse

Model hierarchy

Operation scenario

analysisTim

e horizo

n

Very short term

Short term

System detail

Uncertainty +

+_

_


(Erasmus Mundus)


Operation scenario

probabilistic analysis

Operation scenario

probabilistic analysis

Investment selection and analysis

Tim

e horizo

n

Short term

Medium term

Long term

Content

• Motivation and applications

� Probabilistic operation models

• Uncertainty modeling• Some models


(Erasmus Mundus)


• Some models

Methods

• Important developments in the field of reliability studies taking into account the transmission network– Adequacy assessment


(Erasmus Mundus)


• Extension to cost studies

General structure

Uncertainty

•Demand

•Hydrology

•Equipment

unavailability

•Demand

•Hydro energy

available

•Committed units

•System configuration


(Erasmus Mundus)


Analysis of

operation

snapshots

Results

•Cost evaluation

•Reliability indexes

•Economic indexes

•Technical indexes

•Sensitivities

Methods

Generation + Network

Simulation

Single node generation

Analytical methods

(probabilistic simulation)


(Erasmus Mundus)


Sampling

Monte Carlo simulation

(cost-reliability)

Chronological -Sequential

Enumeration

(reliability)

Random

Electric network subsystem

• Single node• Generation/transmission

– Transportation model (1st Kirchoff’s law)– DC optimal power flow with or without losses– AC optimal power flow– Dynamic aspects


(Erasmus Mundus)


– Dynamic aspects

• Circuits– Branches: lines and transformers.– Nodes: substation buses.

Security criterion in contingency dispatch

• Preventive– Network and/or generation margin, N-1. – Representation in the dispatch model (global optimization, relaxation, scenarios, reserve markets and interruptibility)

• Corrective


(Erasmus Mundus)


• Corrective– Generation response margins– Load redistribution

Other characteristics to model

• Networks operating limits:– Line thermal limits.– Node voltages limits.

• Interruptible contracts• Network emergency operation: e.g., tie and


(Erasmus Mundus)


• Network emergency operation: e.g., tie anduntie, substation reconfiguration

• Violation of preventive security regular criteria in special states (e.g., high cost, emergency)

• Reserves• Exogenous criteria that condition the dispatchoptimality (e.g., fuel quota)

Generation dispatch model

• Optimization

• Simulation + heuristics– Sampling of random parametersLogic rules and pre-established strategies to “optimize”


(Erasmus Mundus)


– Logic rules and pre-established strategies to “optimize” the decisions

Content

• Motivation and applications• Probabilistic operation models

� Uncertainty modeling

• Some models


(Erasmus Mundus)


• Some models

Uncertainty treatment

• Sources– Demand– Contingencies (availability of generation and network elements)

– Unregulated inflows or hydro outputs


(Erasmus Mundus)


–

• Enumeration is not possible by the huge number of states ⇒ Monte Carlo simulation

How many samples are needed?

• Let’s suppose that 25 samples are enough to determine the mean with a small enough confidence interval

• Failure probability– for a generator: 5 %– for a line: 0.5 %


(Erasmus Mundus)


– for a line: 0.5 %

• If I want to obtain 25 samples of– a generator failure I’ll need 500 samples– a line failure I’ll need 5000 samples

• Therefore, I’ll need at least 5000 samples to obtain failures in lines and perhaps non served energy in certain nodes

• A strong computational effort is needed

Stages in Monte Carlo simulation

1. Pseudorandom number generation2. Random variable generation3. Simulation or parameter sampling4. (Variance reduction techniques)


(Erasmus Mundus)


5. Results collection6. Sampling process stop

Composite operation model

SETSETSETSET

cl Line characteristics

/r, x, pmax, efor/

SETSETSETSET

samples number of samples / 1 * 5000 /

t_aux(g) thermal units

h_aux(g) hydro units

ii_aux(i,i) nodes connected by a line

SCALARSCALARSCALARSCALAR

samplevalue sample valueUnit equivalent

Line equivalent

forced outage

rate

Number of

samples


(Erasmus Mundus)


PARAMETERSPARAMETERSPARAMETERSPARAMETERS

efor(g) unit equivalent forced outage rate [p.u.]

POSITIVE VARIABLESPOSITIVE VARIABLESPOSITIVE VARIABLESPOSITIVE VARIABLES

pns(i) power non served [GW]

E_FOBJ ..

fobj =E= SUMSUMSUMSUM[t, f(t) * alfa(t) * q(t) / k(t) + o(t) * q(t)]

+ SUMSUMSUMSUM[h, c(h) * [q(h) - rend(h) * b(h)]] + 300*sumsumsumsum[i, pns(i)];

E_DMND(i) ..

SUMSUMSUMSUM[t $ it(i,t), q(t)] + SUMSUMSUMSUM[h $ ih(i,h), q(h) - b(h)]

- SUMSUMSUMSUM[j $ ii(i,j), p(i,j)]

+ SUMSUMSUMSUM[j $ ii(j,i), p(j,i)] =E=

d(i) - pns(i) ;

pns.up(i) = d(i) ;

Unit equivalent

forced outage

rate

Power non served

PNS cost in the

objective funct

PNS in demand

equationPNS bound

Monte Carlo simulation loop

* Initialization of auxiliary sets* Initialization of auxiliary sets* Initialization of auxiliary sets* Initialization of auxiliary sets

ii_aux(i,j) = ii(i,j) ;

t_aux(g) = t(g) ;

h_aux(g) = h(g) ;

* Loop for all the samples* Loop for all the samples* Loop for all the samples* Loop for all the samples

LOOPLOOPLOOPLOOP (samples,

ii(i,j) = ii_aux(i,j) ;

t(g) = t_aux(g) ;

h(g) = h_aux(g) ;

* Sample of thermal unit availability* Sample of thermal unit availability* Sample of thermal unit availability* Sample of thermal unit availability

LOOPLOOPLOOPLOOP (t_aux(g),

samplevalue = uniform(0,1) ;

Sample loop

Thermal unit availability


(Erasmus Mundus)



t(g) $[samplevalue < efor(g)] = nononono ;

) ;

* Sample of hydro unit availability* Sample of hydro unit availability* Sample of hydro unit availability* Sample of hydro unit availability

LOOPLOOPLOOPLOOP (h_aux(g),


h(g) $[samplevalue < efor(g)] = nononono ;

) ;

* Sample of line availability* Sample of line availability* Sample of line availability* Sample of line availability

LOOPLOOPLOOPLOOP (ii_aux(i,j),


ii(i,j) $[samplevalue < dtl(i,j,'efor')] = nononono ;

) ;

* Solving the problem* Solving the problem* Solving the problem* Solving the problem

SOLVESOLVESOLVESOLVE MGR USING LP MINIMIZING fobj;

$ INCLUDE MSE_MGR_RESULTADOS.INC

) ;

Hydro unit availability

Line availability

DC optimal power flow

solution

Monte Carlo simulation (I)

• It is used when the number of states of the random parameters is very huge (e.g., contingencies)

• Estimate the mathematical expectation of operating costs and/or reliability measures


(Erasmus Mundus)


operating costs and/or reliability measures• Simulate is equivalent to integrate or sample in hyperspace of random parameters with a known probability density function

• Determine sample mean, mean variance, confidence interval.

• Stop sampling when confidence interval is lower than a certain tolerance.

Monte Carlo simulation (II)

• Quadratic behavior (4 times more samples divides by 2 the confidence interval)

• Events with a small probability and a huge value of the objective function cause high variances (it is the usual case of reliability indexes). Therefore, many samples are needed


(Erasmus Mundus)


• Variance reduction techniques– Common random numbers, antithetic variables, control variable, importance sampling, stratified sampling

– Allow to reduce the size of the confidence interval of the mean without disturbing its value for a certain number of samples or, alternatively, achieve the desired precision with a lower sampling effort.

Variance reduction techniques VRT (I)

• Usually, it is impossible to know in advance the variance reduction to be achieved, or even if it is going to be reduced. We have to experiment considering the real system to analyze.

• You have to know the model in detail that reproduces the system behavior.


(Erasmus Mundus)


• The use of VRT can be understood as a way of taking advantage of information about the implied system.

• Imply a computational over-cost to do certain preliminary samples or auxiliary computations in the same simulation process.

Variance reduction techniques VRT (II)

• Common random numbers or correlated sampling or comparative simulation or synchronized pairs– Do sampling for different system configurations with the same set of random numbers being used each one for the same function in sampling process.


(Erasmus Mundus)


same function in sampling process.

• Antithetic variables– It is based on the idea of introducing a negative correlation between two consecutive samples. It consists of the use of complementary random numbers in two consecutive simulations.

Variance reduction techniques VRT (III)

• Control variable– The basic idea is to use the results of a simpler model to predict or explain part of the variance of the value to estimate. A previous computation of the expected value of the control variable is needed. This computation has to be very quick compared to those of the variable to estimate.


(Erasmus Mundus)


very quick compared to those of the variable to estimate.

• Importance sampling– The random variable to estimate is replaced by another with the same mean but different variance. The probability density function used in the sampling process is modified to center it around the area of interest. Sampling probable but not interesting events is avoided.

Variance reduction techniques VRT (IV)

• Stratified sampling– The intuitive idea of this technique is similar to the previous one but in a discrete version. It consists on taking more samples of the random variable in the areas of greater interest. The variance is reduced by concentrating the simulation effort in the more relevant


(Erasmus Mundus)


concentrating the simulation effort in the more relevant strata.

Content

• Motivation and applications

• Probabilistic operation models• Uncertainty modeling

� Some models


(Erasmus Mundus)


� Some models

Some IIT transmission network planning models

• Medium term application– StarNet/RD for different companies in Dominican Republic– SIMUSIS/SIMUMER/SIMUPLUS for REE

• Long term application


(Erasmus Mundus)


• Long term application– PERLA/CHOPIN for REE

StarNet/RD (i) (www.iit.upcomillas.es/aramos/StarNet.htm)


(Erasmus Mundus)


StarNet/RD (ii)


(Erasmus Mundus)


StarNet/RD (iii)


(Erasmus Mundus)


StarNet/RD (iv)


(Erasmus Mundus)


StarNet/RD (v)


(Erasmus Mundus)


StarNet/RD (vi)


(Erasmus Mundus)


StarNet/RD (vii)


(Erasmus Mundus)


StarNet/RD (viii)


(Erasmus Mundus)


StarNet/RD (ix)


(Erasmus Mundus)


StarNet/RD (x)


(Erasmus Mundus)


CHOPIN

• G. Latorre, J.I. Perez-Arriaga CHOPIN, A HEURISTIC MODEL FOR LONG TERM TRANSMISSION EXPANSION PLANNIG IEEE Transactions on Power System, Vol. 9, No. 4, November 1994


(Erasmus Mundus)


PLAER

• de Dios, R., Sáiz, A., Melsión, J.L. y Bassy, A., “PLAER. Strategic Transmission Network Planning”. 11TH Power System Computation Conference, August 1993


(Erasmus Mundus)


PERLA

• J.F. Alonso, A. Sáiz, L. Martín G. Latorre, A. Ramos, I.J. Pérez-Arriaga PERLA: An Optimization Model for Long Term Expansion Planning of Electric Power Transmission Networks IIT-91-009 January 1991 (http://www.iit.upcomillas.es/aramos/papers/COIMBRA.pdf)


(Erasmus Mundus)


SIMUPLUS (i)

• Determine incremental investment needs in transmission network for the medium term in electricity markets Scenario Sampling: Bids & Failures

Market Clearing Procedure: MO model

Scenario Sampling: Bids & Failures

Market Clearing Procedure: MO model


(Erasmus Mundus)


Transmission Adequacy: SO model

Transmission Investment Results

Stop Criterion

reached?

No

Multiobjective Investment Analysis

Yes

Transmission Adequacy: SO model

Transmission Investment Results

Stop Criterion

reached?

No

Multiobjective Investment Analysis

Yes

P. Sánchez-Martín, A. Ramos, J.F. Alonso Probabilistic mid-term transmission planning in a liberalized market IEEE Transactions on Power Systems 20 (4): 2135-2142 Nov 2005

(http://www.iit.upcomillas.es/aramos/papers/TPWRS-00679-2004.pdf)

SIMUPLUS (ii)

1. Monte Carlo sampling:– Demand bids and generation offers– Units and circuits availability– Hydro and wind generation

2. Single node market clearing– Losses included as additional demand

3. Network constraint evaluation penalizing deviations with


(Erasmus Mundus)


3. Network constraint evaluation penalizing deviations with respect to market clearing– DC load flow, flow limits, losses– N-1 contingencies

4. Determine sensitivities (derivative of the objective function with respect to investment):– Improvement in existing circuits– New circuit expansion

SIMUPLUS (iii)

5. Investment multi-attribute analysis– Weigh sensitivities average, confidence interval, validity

range, investment needs, environmental impact, etc.– Investment selection

6. Repeat all the process


(Erasmus Mundus)


6. Repeat all the process

SIMUPLUS (iv)

• 623 nodes and 1021 circuits, 165 thermal units and 76 hydro units. 12 network expansion alternatives. Sampling of 100 scenarios in each stage and

obtain the 3 best alternatives.

Spanish Iterative Investment Ranking

Stag

e

Candidates Sensitivity

mean

[M$/M$]

Confidence

interval

[%]

Validity

range

[MW]

Multi-

attribute

value

No circuit is added (initial stage)

1 431-461 -5.622 8.6 296 1.505

390-403 -3.365 7.9 119 0.767

570-583 -1.254 63.4 131 0.727

Circuit 431-461 is added

2 586-588 -3.275 57.5 138 1.162

390-403 -3.352 7.9 107 0.941

570-583 -1.849 56.8 128 0.897Deviation Penalization Overload PenalizationDeviation Penalization Overload Penalization


(Erasmus Mundus)


Circuits 431-461 and 586-588 are added

3 390-403 -3.633 6.9 157 1.468

570-583 -0.289 39.1 138 0.894

424-520 -2.841 7.9 6 0.638

Circuits 431-461, 586-588 and 390-403 are added

4 570-583 -0.587 51.4 129 1.434

424-520 -2.930 7.8 5 0.821

500-567 -1.784 10.1 30 0.745

Circuits 431-461, 586-588, 390-403 and 570-583 are added

5 457-498 -0.495 19.8 83 1.293

424-520 -3.027 7.6 7 0.933

500-567 -1.665 10.9 21 0.774

No more circuits are added Cumulative Circuits

50

40

30

20

10

0- 431-461 586-588 390-403 570-583

DeviationandOverload

Decrement[%

]

5

4

3

2

1

0

OperationCostDecrement[%]

Deviation Penalization Overload Penalization

Operation Cost

Cumulative Circuits

50

40

30

20

10

0- 431-461 586-588 390-403 570-583

DeviationandOverload

Decrement[%

]

5

4

3

2

1

0

OperationCostDecrement[%]

Deviation Penalization Overload Penalization

Operation Cost

Summary

• Where to use a composite reliability model• Some characteristics to be considered into this model

• Mathematical techniques used to solve the model• Some real applications


(Erasmus Mundus)


• Some real applications

Master Universitario en Sector Eléctrico(Erasmus Mundus)

www.upcomillas.es/mse

Contact: [email protected]

Alberto Aguilera 23, E-28015 Madrid - Tel: +34 91 542 2800 - Fax: +34 91 559 6569 - http://www.icai.upcomillas.es

EMIN: International Master in Economics andManagement of Network Industries

www.upcomillas.es/emin

Contact: [email protected]

emin: international master in economics and management of ... · ii_aux(i,i) nodes connected by a...

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